Question

What are the solutions of 3t + 2 < 7 or -4t + 5 < 1? Graph the solutions and put each solution in interval notation.

Answer 1

`\displaystyle (-∞, 2(1)/(3)) ∪ (1, ∞) \\ \\ 2(1)/(3) > t \:OR\: 1 < t`

Explanation:

3t + 2 < 7 OR −4t + 5 < 1

- 2 - 2 - 5 - 5

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`\displaystyle (3t)/(3) < (7)/(3) \:OR\: (-4t)/(-4) < (-4)/(-4) \\ \\ t < 2(1)/(3) \:OR\: t >1`

**Whenever you divide\multiply by a negative integer, you reverse the inequality symbol given to you initially.

Extended Information on Inequalities

≤, ≥ [dark circle with a dark line (brackets when writing in Interval Notation)]

<, > [light circle with a dashed line (parentheses when writing in Interval Notation)]

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As you can see in the above graph, the graph is connected ALTOGETHER. Be aware that this will not ALWAYS be the case because a majourity of these graphs are seperated, pointing in OPPOSITE directions.